If d = (c - b)/(a - b), then b =

Question

A. (c - d)/(a - d)

B. (c + d)/(a + d)

C. (ca - d)/(ca + d)

D. (c - ad)/(1 - d)

E. (c + ad)/(d -1)

Bunuel · Answer

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GMATinsight · Answer

d = (c - a)/(a - b)

i.e. (a-b) = (c-a)/d

i.e. b = a - (c-a)/d

i.e. b =  /d

Bunuel  Are the options correct???

Bunuel · Answer

There was a typo: it's d = (c - b)/(a - b) NOT d = (c - a)/(a - b). Edited. Thank you for noticing!

pushpitkc · Answer

We are given that d =  \frac{c-b}{a-b}

Cross multiplying, da - db = c - b

db - b = c - ad  ->  b(d - 1) = c - ad  ->  b = \frac{(c - ad)}{(d - 1)}

Therefore, b =  \frac{(c - ad)}{(d - 1)}   (Option D)

Alternate approach 
 
If c=4,b=1,a=2 then d=4-1/2-1 = 3

Now substutiting in the available answer options,

A. (c - d)/(a - d) = (4-3)/(2-3) = -ive

B. (c + d)/(a + d) = (4+3)/(2+3) = 7/5

C. (ca - d)/(ca + d) = (8-3)/(8+3) = 5/11

D. (c - ad)/(1 - d) = (4-6)/(1-3) = -2/-2 = 1
 
 E. (c + ad)/(d -1) = (4+6)/2 = 10/2 = 5   (Option D)

GMATinsight · Answer

d = (c - b)/(a - b)

i.e. da - bd = c-b

i.e. bd - b = da - c

i.e. b (d-1) = da-c

i.e. b = (da - c) / (d-1) or

b = (c - ad)/(1 - d)

Answer: option D

ScottTargetTestPrep · Answer

First, we multiply both sides by (a - b) and expand the left side:

d(a - b) = c - b

da - db = c - b

Now, since our goal is to solve for b, we put all terms containing b on the left side of the equation and all other terms on the right side:

b - db = c - da

On the left side of the equation, factor out the common factor b from both terms:

b(1 - d) = c - da

Divide both sides by (1 - d), and now b is by itself on the left side of the equation:

b = (c - da)/(1 - d)

Answer: D

mawo123 · Answer

I understand the algebraic approach, but I can not get alternative approach. Using your variables I arrived at the correct answer, but when I use the variables 
a=1 , b=2, c=3, and d=-1, I get answer A and D equal to 2. Why can I not use this set of variables?

grgsky · Answer

I can follow your manipulations once I see the solution but how did you know - in two minutes - those were the right manipulations to get to the answer choices?.. I got stuck with b=c-da+db (which is correct but does not correspond to any answer choices...).

hoang221 · Answer

d  =  \frac{(c-b)}{(a-b)}  =>  d(a - b) = c - b  =>  ad - bd = c - b  => 
 b - bd = c - ad  =>  b(1 - d) = c - ad  =>  b  =  \frac{(c-ad)}{(1-d)}

Answer (D)

hoang221 · Answer

hi, ideally in these kind of questions, you'll want to concentrate all the value that related to b on one side of the equation and the rest on the other side. Check my solution above for details

bumpbot · Answer

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If d = (c - b)/(a - b), then b =

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